02-0024.PDF

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World Conference on Earthquake Engineering

October 12-17, 2008, Beijing, China

ONE-DIMENSIONAL RESPONSE OF A BOREHOLE STATION DURING

THE 2005 WEST OFF FUKUOKA PREFECTURE EARTHQUAKE:

OBSERVATION AND SIMUALTION

F. De Martin1, H. Kawase

2and A. Modaressi

3

1

Engineer, Development Planning and Naturals Risks Division, brgm, Orlans. France2

Professor, Disaster Management for Safe and Secure Society, Disaster Prevention Research Institute, Kyoto,

Japan3

Professor, Laboratoire Mcanique des Sols, Structures et Matriaux CNRS UMR 8579, Ecole Centrale de

Paris, Chatenay-Malabry, France

Email: [email protected], [email protected], [email protected]

ABSTRACT :

The objective of this paper is to present a one-dimensional response of a soil column at a borehole stationduring the 2005 west off Fukuoka prefecture, Japan, earthquake. The borehole station is located in Fukuoka

City where the sediments thickness reaches 56 meters. First, we have confirmed that according to the rupture

process the major axis is north 32 degrees east by calculating the observed energy distribution at several

stations around the epicenter. Then we have computed, in the major and minor axes, surface-to-borehole

spectral ratios using the S-wave portion of the main shock and 12 aftershocks. As for the aftershocks, the

fundamental resonant peaks lie in the frequency range of 1.5 to 1.9 Hz, and are quite stable. As for the main

shock, the resonant peak is 1.3 Hz showing a nonlinear effect. To simulate the main shock, we have first

inverted by genetic algorithm S-waves velocities and damping coefficients of the soil column as well as

incident angle of the upcoming wave using Thomson-Haskell propagator matrix for SH and P-SV waves.

Inverted values of S-waves velocities are consistent with the P-S logging provided by CTI Engineering and

inverted incident angle is also consistent with observed particle orbit in the vertical plane. Simulations at theborehole station show a good agreement with observations.

KEYWORDS: borehole observation simulation propagator inversion genetic-algorithm

1. INTRODUCTION

It is now recognized that the ground motions observed at two sites, even within a short distance, are different

from each other because of site effects due to local geology. Hence, the importance of local site geology in

seismic design is nowadays well established and the evaluation of site effects on strong ground motion has been

extensively studied during the last three decades and is thoroughly reviewed (e.g., Aki [1988]).

In order to understand site effects, the one-dimensional (1-D) modeling of soil amplification has been proved to

be a good approximation for most cases. In recent years, 2-D or 3-D effects of basins are found to be relevant

for several cases of strong ground motion (e.g., Kawase and Sato [1992]). However, those effects are essentially

predominant in the low-frequency range ( 1Hz) and since seismic waves with shorter wavelength are more

vulnerable to mutual interference of multiple reflection/refraction and to intrinsic/scattering attenuation, 2-D or

3-D effects in higher frequency would easily disappear. Moreover, it has been shown during two

blind-prediction experiments conducted by the IASPEI/IAEE Joint Working Group on Effects of Surface

Geology on Strong Motions (e.g., Midorikawa [1992]) that precision of the geological structure is more

important than the model dimension. Therefore, we study in this paper the 1-D response of a borehole station by

focusing on the geological structure. 2-D or 3-D effects could be taken into account for further study.

After the 2005 west off Fukuoka earthquake, different studies have been pursued on Fukuoka City basin.Simulations of strong motions within the entire basin using 1-D theory showed that the largest PGV (about 80

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cm/s) was located in the northeast side of the Kego fault where the Quaternary sediments are the deepest (e.g.,

Satoh and Kawase [2006]).

In this study, we first demonstrate that the major axis of the main shock within Fukuoka City basin is

approximately the fault perpendicular direction (N32E) by calculating the observed energy distribution at 22stations within 60 km from the epicenter. Then we compute, in the major and minor axes, observed

surface-to-borehole spectral ratios at CTI borehole station using the S-wave portion of the main shock and 12

aftershocks. Then, to simulate the main shock, we invert by genetic algorithm S-waves velocities and damping

coefficients of the soil column as well as incident angle of the upcoming wave using Thomson-Haskell

propagator matrix method for SH and P-SV waves (e.g., Thomson [1950], Haskell [1953]).

2. OBSERVATION

2.1 Overview of the Strong Ground Motion

Fukuoka City is located on the northern part of Kyushu Island, southwestern part of Japan (Figure 1 left panel).The 2005 west off Fukuoka prefecture earthquake with JMA (Japanese Meteorological Agency) magnitude MJ

of 7.0 (Mw = 6.6) and focal depth of 9.2 km occurred on 20 March 2005 in the north coast of Kyushu Island

within the prolongation of the Kego fault. Figure 1 right panel shows the Kego fault (solid line at the

southwestern side of the station FKO006) and accelerograms at some stations surrounding the epicenter. We can

see at a glance that the accelerogram at FKO006 exhibits longer vibration periods than other stations. This

observation is consistent with the geology at station FKO006 composed of Quaternary sediments of around 30

meters depth. Other stations situated on engineering bedrock show accelerograms with shorter periods.

Figure 1: Left panel: localization of Fukuoka City, northern part of Kyushu Island, Japan. Right Panel: location

of the Kego fault (solid line at the south-western side of the station FKO006) and accelerograms recorded at

stations surrounding the epicenter (pointed out by a star) of the Fukuoka earthquake.

2.2 Energy Distribution and Theoretical Radiation Pattern

We first confirm the major and minor axes using the energy distribution in the horizontal plane at 22 stations.

The energy distribution, given by Takizawa [1982] and successfully used to confirm major axis of strong

motion by Kawase and Aki [1990], consist of calculating the total power and cross spectra of the two orthogonal

components n (referring to north) and e (referring to east) in the frequency range of interest:

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where Snn() is a velocity power spectrum of the n direction and Sne() is a velocity cross power spectrum

between the n and e direction, and so on. Then, the energy in the direction measured clockwise from the

n-axis can be obtained as

This energy distribution will be two elliptic lobes in line with the major axis if the ground motion is

unidirectional, while it will become a single circle if the ground motion is not directional at all.

Fukuoka earthquake being a strike-slip crustal earthquake with a strike direction equal to N122E, a dip angle of

89 and a rake angle of -11 (e.g., Asano and Iwata [2006]) we can first plot theoretical far-field radiation

pattern of the so-called Double Couple mechanism in an infinite homogeneous medium to have in mind

predominant direction of motion. Figure 2 shows radiation pattern for P- and S-waves and for SH and SV

components. The fault plane and the auxiliary plane are nodal lines for P-wave whereas they are predominant

plane for S-wave. By decomposition of S-wave into SH and SV component, we see that SH component is

predominant in the fault plane and in the auxiliary plane whereas these planes are nodal lines for SV component.

Figure 3 shows the energy distribution calculated in the horizontal plane for records observed at 22 stations (it

should be noted that if necessary, energy distributions have been corrected by rotation of sensors). Depending

on stations, the observation shows more or less a good agreement with the solution of the double couple point

source model. The energy distribution in the fault plane at the stations FKOS02, FKOS05, FKOS06 and

FKO009 shows a good coherence since it exhibits a major axis perpendicular to the fault plane (i.e.,

predominance of SH-component). The same agreement can be seen for the auxiliary plane, where stations

SAG001, SAGH01 and FKOH09 exhibit the same predominance. However, within Fukuoka City, we can notice

that the energy distribution of FKO006, FKOS01 and CTI is slightly rotated toward north. This rotation could

be due to an arrival of later phases (e.g., trapped waves (Li and Leary [1990])) after the main train of S-wave.

2.3 Surface-to-Downhole Spectral Ratios

Records of the borehole station with a sample frequency of 100 Hz have been provided by CTI Engineering Co.,

Ltd which is located where the thickness of sediment reaches 56 meters. Two sensors are situated below their

base-isolated building, one at the free surface and the other one at 65 meters below the free surface embedded in

the bedrock. As the building is base-isolated, soil-structure interaction has been neglected and the surface

ground motion has been considered as a free field ground motion. A section cut realized at 210 meters on the

northern part of the borehole station is shown in Figure 4 left panel (Geological Survey Association of Kyushu,

Fukuoka soil map [1981]). The associated 1-D velocity profile is shown in Figure 4 right panel. The top 17

meters mainly consists of sand (Arae formation) whose S-wave velocity increases from 150 m/s to 361 m/s, and

then 8 meters of clay are present whose S-wave velocity is around 230 m/s. Then follow thin layers of sand andclay and 13 meters of sand (Hakata formation), whose S-wave velocity ranges between 292 m/s and 495 m/s.

Below, the engineering bedrock is made of mudstone dating from the pre-Tertiary period of Cenozoic era whose

S-wave velocity has been supposed as 650m/s. For computation of spectral ratios, the following procedure has

been used:

accelerograms have been band-pass filtered in the frequency range [0.1-10] Hz with a 6 th orderButterworth filter;

a cosine shape of 25% of the time window has been applied at both ends of the selected S-wave portion; to compute the Fast Fourier Transformation, a number of data samples N equal to 4,096 has been

chosen to have a fine frequency resolution;

Fourier spectra have been smoothed with a spectral Parzen bandwidth of 0.4 Hz in order to removenon-physical peaks.

Figure 5 exposes spectral ratios computed for the main shock and the aftershocks in fault perpendicular andfault parallel directions.

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Figure 2 : Theoretical radiation pattern of far-field

wave for a double couple point source model in an

infinite homogeneous medium oriented as

followed: strike = 122, dip = 87 and rake = -11.Panels (a) and (b) show P- and S-wave radiation

pattern, respectively. Panels (c) and (d) expose SV

and SH component of the S-wave, respectively.

Top panels show a 3-D view of the radiation

patterns and bottom panels show them mapped

into the horizontal plane. The panel (d) clearly

exposes a predominance of the SH-component in

the fault plane and in the auxiliary plane.

Figure 3: Energy distribution in the horizontal plane (NS-EW) for the records observed at 22 stations within 60

km from the epicenter. The principal axis measured clockwise from the north (see station NGS023) has +/- 180ambiguity. The energy distribution is calculated from velocity power spectra which are derived from NS and

EW components of velocity seismograms (the entire record has been used to compute the power spectra). The

frequency range used to integrate a power spectrum is 0.1 to 10 Hz. Solid lines represent the energy distribution

calculated at the free surface sensor and dash lines that of the downhole sensor. The rectangle on the left-hand

side panel denotes the area shown on the right-hand side panel. The approximate location of the Kego fault is

represented by a solid straight line (both panels) and the epicenter of the earthquake by a star (left panel only).

Figure 4: Left panel: east-west section cut located at 210 meters on the northern part of CTI borehole station.

The vertical axis has been exaggerated. The borehole station is indicated by a solid line and the sensors are

represented by two points along this line. The upper sensor is located at the free surface, below the base

isolation and the downhole sensor is embedded in the bedrock. Right panel: 1-D velocity profile along theborehole station provided by CTI Engineering Co., Ltd.

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Figure 5: Spectral ratios computed at CTI borehole

station (left-panel: fault perpendicular direction;right-panel: fault parallel direction). The spectral

ratio of the main shock is plotted with a thick line.

For the aftershocks,whose PGAs range from 2 cm/s2 to 32 cm/s2, we notice that spectral ratios exhibit afundamental mode around 1.5 Hz and 1.9 Hz. The second mode is present around 3.7 Hz. Other higher modes

are present around 6.0 Hz and 8.5 Hz. During the main shock, the fundamental mode is not clearly visible on the

fault perpendicular direction. However, it is clear on the fault parallel direction and its frequency is around 1.3

Hz. Higher modes are visible for the fault perpendicular direction but not so much for the fault parallel

direction.

The shift of frequency from 1.9 Hz during aftershocks to 1.3 Hz during the main shock suggests a nonlinear

behavior of the soil. This nonlinear behavior can be seen by calculating the cross-correlation between the

downhole and surface sensors(e.g., Kawase and Sato [1992]). Figure 6 left panel exposes the time delay againstthe PGA. As the PGA increases, the time delay increases as well; this denotes a decrease of the S-wave velocity

and thus points out a nonlinear effect. Middle and right panel show an example of cross-correlation calculated

for the main shock and for an aftershock. The positive peak between 0 and -0.5 second denotes the time delay of

the S-wave recorded at the free surface sensor with respect to the S-wave recorded at the downhole sensor. A

larger time delay is seen for the main shock.

Figure 6: Left panel: Time delay plotted against PGA. Middle and right panel: Example of cross correlation

computed on the S-wave part of the main shock and of an aftershock.

3. SIMULATION

3.1 Inversion of S-wave Velocities and Damping Coefficients Considering Obliquely Incident Wave

Before simulating the main shock, we have inverted by genetic algorithm (e.g., Goldberg [1989]) S-wave

velocities (Vs) and damping factors of the soil column as well as incident angle of the upcoming wave using

Thomson-Haskell propagator matrix for SH and P-SV waves. The original P-S logging from CTI has been

divided into 5 parts by taking into account S-wave velocity similarity (on 56 meters of sediment, 43 have been

inverted to limit number of parameters to invert). Each part is affected by coefficients to be optimized for

S-wave velocities and damping factors. Initial values for S-wave velocities are those from P-S logging.

Coefficients to optimize were constrained in the range [0.5-1.2] with a discretization of 0.0055 (1.0 being P-S

logging values). Damping factor has been chosen of the form h0f

, with f the frequency (e.g., Satoh et al.

[2001]). Initial values are 0.05 for h0 and 0.4 for. The interval for h0 and is [0.3-2.5] with a discretization of

0.07 and incident angle precision is 0.96. A general scheme of the optimization by genetic algorithm is show inFigure 7 left panel. The initial population step generates N individuals representing coefficients to be optimized

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in binary format (information contained in one individual represent the first 43 meters of the soil column plus

the incidence angle). Then, during the evaluation step, theoretical spectral ratios are computed for each

individual and the objective function for an individual is computed by the following formulae:

E(x) =

where H0

SH and H0

PSV are observed fault perpendicular and fault parallel surface-to-borehole spectral ratios

represented theoretically by HSH (the ratio of SH-waves at the free surface to the obliquely incident SH-waves at

the bedrock) and HPSV (the ratio of the horizontal components of SV-waves and P-waves at the free surface to

the horizontal component of SV-waves at the bedrock) as assumed by Satoh [2006]. x is the vector to be

optimized and feSH

, fsSH

, fePSV

and fsPSV

the frequency range of integration for SH ratio and PSV ratio respectively.

In our study, we have chosen 2.7, 7.4, 0.5 and 5.0, respectively, based on the clarity of predominant peaks.

Figure 7: General scheme of optimization by genetic algorithm (left panel). Evolution of objective function

with respect to population during the inversion of the soil column of the main shock (right panel).

If the termination criterion is not reached (i.e., small value of E(x) or large number of population) then half of

the population P is selected by roulette-wheel to constitute parents who give birth to offspring through the

crossover step (uniform crossover has been used for the optimization). Finally, very few or no individuals are

mutated with a low probability (i.e., one or more of their bytes are changed from 1 to 0 orvice versa) to create

the new population P+1 and so on. Evolution of the objective function for inversion of the main shock is

exposed in Figure 7 right panel; inverted and observed SH and P-SV ratios for the main shock and two inverted

and observed P-SV ratios of aftershocks are shown in Figure 8.

Figure 8: Two left panels: observed and inverted spectral ratios of the main shock for fault perpendicular and fault

parallel direction. Two right panels: observed and inverted ratios for two aftershocks for fault parallel direction.

Inverted values of Vs, h0 and are plotted together with their initial values in Figure 9. We can see that for the

main shock inverted values of Vs are consistent with PS-logging values except around -17 meters and -30

meters where P-S logging shows high local values. Inverted shear wave velocities for the two aftershocks

clearly exhibit higher values than for the main shock, showing the evidence of nonlinear behavior of the soil

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during the main shock.

Figure 9: Inverted values of the top 43 meters and

initial values of the entire column for Vs (left panel),

h0 (middle panel) and - (right panel). For Vs only,

inversions for two aftershocks are plotted as well

(lines with points). Around 40 meters depth, the ratio

of inverted S-wave velocity for aftershocks to P-S

logging velocity is around 220%.

As an example, for the main shock, the inverted incidence angle is 8.7 and is consistent with the particle orbits

on a vertical plane calculated from borehole accelerograms as shown in Figure 10.

Figure 10: Particle orbits on a vertical plane calculated from borehole accelerograms at the onset of S-wave

portion of the main shock. The orbits are calculated from band-pass filtered waves in the frequency range of

interest.

3.2 Simulation of borehole and free surface waveforms

Using inverted SH and P-SV ratios, we have simulated borehole seismograms using free surface records and

vice versa. Simulations are presented in Figure 11. The downhole simulation in N32E direction agrees fairly

well with observation whereas the E32S simulation tends to overestimate PGVs. Agreement for free surface

simulation is still reasonable; however, PGVs are overestimated for the N32E direction.

Figure 11: Simulation of borehole seismograms (left panels) and free surface seismograms (right panels).

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4. CONCLUSION

We have analyzed the one-dimensional response of CTI borehole station during the 2005 west off Fukuoka

prefecture earthquake. We have first found that major and minor axes were N32E and E32S, respectively, by

computing energy distribution at several stations around the epicenter. Then, thanks to observedsurface-to-borehole spectral ratios, we have inverted S-waves velocities, damping factors and incidence angle

via Thomson-Haskell propagator matrix method. Simulations have been performed and reasonably reproduced

observations; however, further simulations should be done to understand overestimation of PGVs.High valuesof inverted Vs for the two aftershocks suggest that further inversions should be done on the entire soil column.

We would like to express our sincere thanks to CTI Engineering Co. Ltd. for allowing us to analyze their data.

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